Wasserstein distance is a measure of dissimilarity between two probability
measures, arising from optimal transport; see e.g. [1]}, [2]}. Due to its desirable convexity and convergence features, Wasserstein
distance is considered as an important measure of dissimilarity
in many applications, ranging from computer vision and machine learning to Seismic and
Bayesian inversion;
see e.g. [3]}, [4]}, [5]}, [6]}.
The application of Wasserstein metric may however be
limited to cases where the probability measures are supported on
low-dimensional spaces, because its numerical computation can quickly become prohibitive
as the dimension increases; see e.g. [3]}.
